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Common tangent to two circles

Two circles touch externally at P. A direct common tangent AB to two circles touch the circles at A and B. Then the measure of angleAPB is

Two circles touch each other extenally at the point A. A common tangent drawn to two circles at the point A is a "______" common tangent. (direct/ transverse)

The length of a common internal tangent to two circles is 5 and a common external tangent is 15, then the product of the radii of the two circles is :

The length of a common internal tangent to two circles is 5 and a common external tangent is 15, then the product of the radii of the two circles is :

In Figure, two circles touch each other at the point C . Prove that the common tangent to the circles at C , bisects the common tangent at P and Q .

In the figure, two circles touch each other at the point C.Prove that the common tangents to the circles at C, bisect the common tangents at P and Q.

The length of common internal tangent to two circles is 7 and that of a common external tangent is 11. Then the product of the radii of the two circles is